Method and System for an Estimator Using Estimated Mean and Covariance

Abstract

An estimator system where unknown values are represented as a plurality of vectors in multi-dimensional space is disclosed. The statistics of the vectors constitute a mean vector and a covariance matrix. A mean vector and a covariance matrix are estimated from a database of known values. Estimated values can then be predicted using the mean vector and the covariance matrix.

What is claimed is: 
     
         1 . A method of predicting an unknown value comprising the steps of: retaining a set of observed values on a computer storage device; accessing the set of observed values from the computer storage device; calculating a mean vector, via a computer processor; estimating a single covariance matrix from the set of observed values; initializing the covariance matrix using the equation R=N −1/2 SN −1/2 , where S denotes an un-normalized sample covariance matrix and elements of the diagonal matrix N denote the number of times each observed value was observed, predicting the unknown value using the mean vector and the covariance matrix when the unknown value is absent from the set; and providing the predicted value to an end user. 
     
     
         2 . The method of  claim 1 , wherein the mean vector is estimated using a stochastic gradient descent approach. 
     
     
         3 . The method of  claim 1 , wherein the covariance matrix is estimated using a stochastic gradient descent approach. 
     
     
         4 . The method of  claim 1 , wherein the prediction of an unknown value is by using a minimum means squared error predictor. 
     
     
         5 . The method of  claim 1 , wherein calculations are performed using basic linear algebra subroutines. 
     
     
         6 . The method of  claim 1 , wherein the covariance matrix is estimated using an expectation maximization algorithm. 
     
     
         7 . The method of  claim 1 , further comprising the step of continuously updating the estimation of the covariance matrix. 
     
     
         8 . The method of  claim 7 , further comprising the step of checking for convergence and if there is convergence halting the continuous updating of the estimation of the covariance matrix and saving the estimated mean vector and covariance matrix. 
     
     
         9 . The method of  claim 1 , further comprising the step of calculating a confidence rating from at least one portion of the covariance matrix. 
     
     
         10 . A system for predicting an unknown value comprising:
 at least one processor with a memory and in communication with at least one database, wherein the database includes a set of observed values;   at least one application stored in the memory and capable of being executed by the processor to perform the following operations:
 accessing the set of observed values from the computer storage device; 
 calculating a mean vector; 
 estimating a single covariance matrix from the set of observed values; 
 initializing the covariance matrix using the equation R=N −1/2 SN −1/2 , where S denotes an un-normalized sample covariance matrix and elements of the diagonal matrix N denote the number of times each observed value was observed, 
 predicting the unknown value using the mean vector and the covariance matrix when the unknown value is absent from the set; and 
 providing the predicted value to an end user. 
   
     
     
         11 . The system of  claim 10 , wherein at least one portion of the covariance matrix is used to calculate a confidence rating. 
     
     
         12 . A method of predicting an unknown value comprising the steps of:
 retaining a set of observed values on a computer storage device;   accessing the set from the computer storage device;   estimating a covariance matrix from the set of observed values using the equation R=N −1/2 SN −1/2 ;   predicting the unknown value using the covariance matrix when the unknown value is absent from the set; and   providing the predicted value to an end user.   
     
     
         13 . The method of  claim 12 , further comprising the step of calculating a confidence rating from at least one portion of the covariance matrix. 
     
     
         14 . A system for predicting an unknown value comprising:
 at least one processor with a memory and in communication with at least one database, wherein the database includes a set of observed values;   at least one application stored in the memory and capable of being executed by the processor to perform the following operations:   accessing the set of observed values from the computer storage device;   calculating a mean vector;   estimating a covariance matrix using a sample covariance matrix, wherein the sample covariance matrix is pre-multiplied and post-multiplied by a diagonal matrix whose elements denote the inverse of the square root of the number of times each observed value was observed;   predicting the unknown value using the mean vector and the covariance matrix when the unknown value is absent from the set; and   providing the predicted value to an end user.   
     
     
         15 . A method of predicting an unknown value comprising the steps of:
 retaining a set of observed values on a computer storage device;   accessing the set from the computer storage device;   estimating a covariance matrix given by an sample covariance matrix, wherein the sample covariance matrix is pre-multiplied and post-multiplied by a diagonal matrix whose elements denote the inverse of the square root of the number of times each observed value was observed;   predicting the unknown value using the covariance matrix when the unknown value is absent from the set; and   providing the predicted value to an end user.